Reconstruction-based methods aim at reconstructing the entire time-series, as presented in Section REF .
Shallow reconstruction-based time-series anomaly detection methods [1]}, [2]}, [3]} have mainly adopted Principal Component Analysis [4]} (PCA) or its variants such as kernel PCA (kPCA)  [5]}. These approaches estimate an orthogonal projection, then compute a reconstruction error between the original and reconstructed time-series. Lately, Auto-Encoders (AE) [6]} have been introduced as the deep learning-based counterpart of PCA. Unsurprisingly, the latter has been adopted in the context of anomaly detection in time-series [7]}. For example, Lin et al. [8]} introduce a Long-Short Term Memory Variation Auto-Encoder (LSTM-VAE) architecture. While the Variation Auto-Encoder architecture (VAE) is used for learning robust representations, a Long Short-Term Memory (LSTM) network allows modeling temporal dependencies. Generative Adversarial Networks (GAN) have also been proposed as a reconstruction-based method. In [9]}, Audibert et al. attempted to take the best of both worlds. In particular, they introduced adversarially trained autoencoders for detecting anomalies in time-series.
